Synchronization, Oscillator Death, and Frequency Modulation in a Class of Biologically Inspired Coupled Oscillators

Frontiers in Applied Mathematics and Statistics

Franci, Alessio¹  Lara-Aparicio, Miguel⁴  Herrera-Valdez, Marco Arieli⁸  Padilla-Longoria, Pablo⁹ 

[1] Departamento de Matemán en Matemánica, Instituto de Investigaciónoma de Ménoma de Mexico, Mexico;ticas Aplicadas y Sistemas, Universidad Nacional Autóticas y Mecáticas, Facultad de Ciencias, Universidad Nacional Autóxico, Mexico

关键词: Circadian Rhythm;    synchronization;    Nonlinear oscillators;    Fokker-Planck;    Hopf bifurcation;   

DOI  :  10.3389/fams.2018.00051

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength and noise play in the synchronization of a system of nonlinear, linearly coupled oscillators. First, we study a deterministic version of the model, capturing the cellular biological level, to find plausible regions in the parameter space for which synchronous oscillations in coupled pacemaker neurons emerge. Second, we focus on studying how noise and coupling interact in determining the synchronized behavior between various interacting neuronal populations, each modeling an endogenous circadian clock. To do so, we leverage the Fokker-Planck equation associated with the system. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used as a guide to further study coupled oscillations in biophysical nonlinear models.

【 授权许可】

CC BY